光學膜乾燥製程中物性預測與調控

Optical and Mechanical Properties of Cast-Dried Polyimide Films

陳柏儒(Po-Ju Chen)

指導教授 ： 劉大佼

國立清華大學/工學院/化學工程學系/博士(2009年)

https://doi.org/10.6843/NTHU.2009.00274

摘要

本研究之目的為探討高分子塗膜在乾燥時所引起的一些物理性質變化，以外平面雙折射(out-of-plane birefringence, OPBR)與塗膜捲曲(curling)為主，此兩現象導因於乾燥過程中產生的殘餘應力。塗膜捲曲是塗膜與基材向塗膜面(coated side)或非塗膜面(uncoated side)彎曲的現象。一般而言乾燥時溶劑揮發使塗膜體積收縮產生殘餘張應力(residual tensile stress)，因此塗膜向塗膜面彎曲。微觀而言，此張應力同時也會誘導高分子鏈平躺於塗膜平面的排列，此微結構使塗膜在垂直塗膜平面與水平塗膜平面方向的折射率不同，也就是產生外平面雙折射。
為解決此問題，本研究建立包含理論與實驗之工具，分析乾燥製程操作變數對OPBR與捲曲之影響，以提供乾燥製程最好的準則。實驗部分，選擇溶劑型的可溶性聚亞醯胺高分子(polyimide, PI)進行分析；聚亞醯胺高分子在光電產業上有著極大的運用，但乾燥製程對其物理性質變化的影響卻尚未被研究。本研究之實驗探討乾燥製程對PI高分子之應力、雙折射與塗膜捲曲等物理性質的影響，同時觀察乾燥製程的操作視窗(operating window)，找出製程條件控制物性的範圍與極限。
理論方面，要計算乾燥應力，必須求解質量平衡方程式(mass balance equation)、能量平衡方程式(energy balance equation)、固化後之黏彈力學方程式(viscoelastic equations)；而從光彈效應(stress-optical rule)與捲曲模型(curling model)則可計算應力造成雙折射與塗膜捲曲之變化量。本研究建立了一維模型與簡單模型來計算乾燥應力及其對於雙折射與捲曲影響之預測。一維模型之統御方程式為完整的質量平衡、能量平衡以及黏彈力學方程式；以有限元素法進行離散後以Fortran程式撰寫進行計算。在三個假設下可簡化一維模型之統御方程式變成簡單模型，首先假設應力起始前塗膜內擴散速率遠大於揮發速率，因此塗膜內濃度保持均勻；再假設固化後膜厚不改變；第三假設塗膜於應力起始後為一均勻黏彈體，其形變遵守一簡單的黏彈模型。
本研究發現，一維模型可準確預測乾燥應力及其對雙折射與捲曲之影響，但一維模型計算時間較長，也無法提供物理意義與解釋。簡單模型由於方程式簡單，可解釋乾燥應力影響物性之物理機制，且所需計算時間短；但其計算準確度較差，尤其不適於預測快速乾燥極限下之結果。本研究亦進行線上(on-line)之實驗與理論比較，證明本研究所建立之理論不僅適用於試驗性(pilot)之實驗，亦可用於工業界之生產線上。乾燥實驗中也找出了乾燥製程能形成均勻液膜的乾燥操作視窗，此視窗限制了乾燥製程對雙折射與捲曲現象操控之極限，過高的乾燥溫度與濕膜厚度皆會使塗膜產生乾燥缺陷。

關鍵字

雙折射 ； 捲曲 ； 應力 ； 乾燥 ； 可溶性聚亞醯胺 ； 建模 ； 操作視窗

並列摘要

The objective of this research is to investigate some physical properties arising during the drying of polyimide film, namely birefringence and curl, both are caused by drying-induced stress. Curl is an out of plane displacement toward coated side or uncoated side at the edges of substrate. In general, coated film tends to shrink during drying and this shrinkage is inhibited by adherence to the substrate, which causes the build-up of a residual tensile stress and forces substrate to curl toward coated side. In microscopic viewpoint, this tensile stress also makes polymeric chains orientation parallel to the coating plane, which result in the difference between the refractive indices parallel and perpendicular to the coating plane, and that is the out-of-plane birefringence (OPBR).
In this paper, the drying-stress induced birefringence and curl of soluble polyimide films was experimentally and theoretically investigated. The experimental results of OPBR and curl have been examined, and an operating window which is a region for stable and uniform film formation was also determined experimentally.
In order to calculate the drying stress, the mass balance equation, the energy balance equation and the viscoelastic equation have to be solved, and then birefringence and curl can be evaluated by the stress-optical rule and the curling model. A one-dimensional (1D) model and a simple model have been developed to predict the drying stress. All governing equations of the mass balance, the energy balance and the viscoelastics are concluded in the 1D model. The computer aided solutions by the finite element method (FEM) were found. Three assumptions that would lead the simplification of the 1D model to reduce it to a simple model. The first assumption is that at the early stage of drying process, there is no concentration gradient inside the film. The second is that the variation of film thickness is negligible after stress built-up. The third is that after stress built-up, the coating material is a homogeneous viscoelastic material and deforms following a modified Maxwell model consisting of a spring connected to two parallel elements: a dashpot and a stick/slip. Because of the simplified governing equations, the simple model can be solved by the Excel spreadsheet.
The predictions of 1D model are in reasonable agreement with experimental results especially for the substrates with high surface energy such as glass, but the model itself is rather complicated. On the other hand, although simple model does not predict the results as accurate as 1D model, it thus provides some physical insight on the formation mechanism of drying stress and is much easier to apply. One just has to be careful with two cases, i.e., rapid drying and large film thickness variation after built-up concentration.
On-line experiments were also carried out and the results were compared with the theoretical models, it was found that the theoretical predictions are also reasonably accurate. An operating window which is a region for stable and uniform film formation was also determined experimentally, which also put the limit of drying-controlled OPBR and curl.

並列關鍵字

birefringence ； curl ； stress ； drying ； soluble polyimide ； modeling ； operating window

參考文獻

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